Coxeter complexes and graph-associahedra |
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Authors: | Michael Carr |
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Affiliation: | a University of Michigan, Ann Arbor, MI 48109, USA b Williams College, Williamstown, MA 01267, USA |
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Abstract: | Given a graph Γ, we construct a simple, convex polytope, dubbed graph-associahedra, whose face poset is based on the connected subgraphs of Γ. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves. |
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Keywords: | primary, 14P25 secondary, 05B45, 52B11 |
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